Quotations

The theory of self-adjoint operator was created by von Neumann to fashion a
framework for quantum mechanics. [...] I recall in the summer of 1951 the
excitement and elation of von Neumann when he learned that Kato has proved the
self-adjointness of the Schroedinger operator associated with the helium atom.
And what do the physicists think of these matters? In the 1960s Friedrichs met
Heisenberg, and used the occasion to express to him the deep gratitude of the community
of mathematicians for having created quantum mechanics, which gave birth
to the beautiful theory of operators in Hilbert space. Heisenberg allowed that this was
so; Friedrichs then added that the mathematicians have, in some measure, returned
the favor. Heisenberg looked noncommittal, so Friedrichs pointed out that it was
a mathematician, von Neumann, who clarified the difference between a self-adjoint
operator and one that is merely symmetric."What's the difference", said Heisenberg.

Contrary to a widespread belief, mathematical rigor, appropriately applied, does not necessarily
introduce complications. In physics it means that we replace a traditional and often antiquated language by a precise but necessarily abstract mathematical
language, with the result that many physically important notions formerly shrouded in a fog of words become crystal clear and of surprising simplicity.

On quantum theory, Eur. Phys. J. D (2013) 67: 238 One of the most lucid and scientifically honest recent expositions of quantum theory by B-G. Englert, one of the last PhD students of Julian Schwinger. Some of the so-called paradoxes of quantum mechanics are analyzed and deconstructed.

What is a state vector? American Journal of Physics 52, 644 (1984) This and the next article are from the late Asher Peres, one of the most profound modern thinkers about quantum mechanics (see his celebrated book above). In this article Peres shows that "[...] a state vector represents a procedure for preparing or testing one or more physical systems. No "quantum paradoxes" ever appear in this interpretation."